Perceptions and interpretations of colour and colour comparisons are highly subjective and can depend on the observer's eye fatigue, age and other physiological factors. Instruments have been designed that can explicitly identify a colour by measuring a sample of the colour and comparing the measured colour to references or standards in a completely objective and accurate manner. These instruments can differentiate a colour from all other colours and can assign the colour a numeric value within a colour system (or colour space).
As is well known, colour is typically described utilising three elements: hue, chroma (also known as saturation) and value (also known as lightness). Hue and chroma are often illustrated in chromaticity diagrams that show colours represented in a horizontal plane. The colour spectrum that humans may perceive forms an irregular shape on this plane: hue varies with angle about an origin of the colour space and chroma varies with distance from the origin. Zero saturation is shown at the origin and this reference point is often called the white point. Pure hues are shown at the edge of the irregular shape with the hues changing as you travel around the edge. Diagrams showing a full colour space often represent hue and chroma in the horizontal plane as described above and represent lightness in the vertical direction. This may be envisaged as a cylindrical co-ordinate system with lightness being the vertical co-ordinate, chroma being the horizontal co-ordinate and hue being the angular co-ordinate.
Various colour spaces exist for the classification of colours, including those defined by the CIE (Commission Internationale de l'Eclairage). These colour spaces include CIEXYZ, CIELAB and CIELUV. CIEXYZ uses three tristimulus values, XYZ. Y relates to lightness but X and Z do not correlate to any visual attributes. To address this, the CIE designated chromaticity coordinates xy which can be correlated to chroma and hue, and which are derived from the tristimulus values, XYZ. These are convenient for use with chromaticity diagrams mentioned above. One issue with the xy chromaticity diagram is that different colours are not uniformly distributed. In an attempt to solve this problem, the CIE recommended two alternate approximately uniform colour spaces: CIE 1976 (L*a*b*) or CIELAB, and CIE 1976 (L*u*v*) or CIELUV.
In CIELAB, the colour space is defined by a Cartesian co-ordinate system. L* denotes lightness and is plotted on the z axis, a* denotes the red/green value and is plotted on the x axis and b* denotes the yellow/blue value and is plotted on the y axis. The resulting diagrams are as described above: the xy plane corresponds to a chromaticity diagram with saturation varying with distance from the origin and chroma varying with the angle about the origin. CIELUV is similar with L* denoting lightness, u* denoting the red/green value and v* denoting the yellow/blue value. CIELAB and CIELUV differ in the mathematical equations that define the colour spaces.
While both CIELAB and CIELUV use colour spaces defined by Cartesian co-ordinates, polar coordinate versions exist to specify colours in a cylindrical space and relate them to colour attributes. CIELCH is such an example. In this colour space, L* denotes lightness and is the z axis value, C* denotes the chroma value and is the distance from the origin, and h denotes the hue value and is the angular value.
With such colour spaces, it is possible not only to measure a colour, but also to measure the differences between colours. That is, a vector from the co-ordinates of one colour to the co-ordinates of another colour may be used to specify the difference in the two colours. The length of the vector represents the separation and hence distance between the colours. Knowing the colour difference can be useful during colour grading. For example, in colour grading, the colour of a sample relative to a set of known standard colours may be wanted, along with by how much the sample differs from the closest standard colour or colours. This may be used to determine whether a sample is within a specified tolerance of a desired colour. The specification of colours within CIELAB, CIELUV and CIELCH colour spaces allows colours to be compared in this way.
There are many known ways of measuring colour that may be employed according to circumstance. Some ways make use of light reflected from a sample, for example from a solid sample like paper or an opaque liquid sample like paint, while others make use of transmitted light, for example from a liquid sample like an oil or a beer. Other factors affect the colour measurement, such as the illuminant, the angle of the observer (for example 2° or 10° from the illuminant) and the sample spacing (for example taking readings every 5 nm or every 10 nm). Standards are available that set out how measurements should be taken and hence allow comparisons to be made objectively, for example those set out by ASTM International of Pennsylvania, USA. One example is ASTM E308 which defines standard practice for computing colours of objects by using the CIE system. Standards are also defined for determining colour differences. ASTM D2244 defines standard practice for calculation of colour tolerances and colour differences from instrumentally measured colour co-ordinates.
Colorimeters are available that measure the colour of a sample automatically. The colorimeter may also identify the nearest reference or standard colour to the sample, and may also provide the colour difference between the sample colour and the nearest reference colour. Usually, the colorimeter identifies the colours by providing the colour co-ordinates for the sample in a colour space rather than providing a display of the colours. This reflects the expense of providing a colour display on the colorimeter, and also problems in achieving an accurate reproduction of a colour on the display.
In particular, electronic visual displays can display only a limited range of colours, known as the gamut of the display. This gamut is generally smaller than the range of colours that may be perceived by the human eye. A gamut boundary defines the distinction between colours that may be reproduced by the display and hence are in-gamut, and colours that may not be reproduced and so are out-of-gamut. The gamut may be plotted on a chromaticity diagram such that the gamut boundary may be visualised. Typically, the gamut boundary forms an irregular shape.
Hence, there is a particular problem when a sample colour is outside of the gamut of the display. Accordingly, there is a desire to display colours on an electronic visual display that allows comparison of colours and that is not affected by the display gamut.